Scattering of acoustic phonons by rare earth substitutional atoms in yttrium aluminum garnets

The diffusive maxima of phonon signals, and in particular their arrival timest _m are examined for a number of solid solutions of rare earth atoms in yttrium aluminum garnets. The phonon pulses are generated by metallic films of the characteristic lengthl _h heated by current pulses to the temperatureT _h slightly higher than the ambient temperatureT. The injected phonons travel in wafers of the thicknessL _z. They are scattered by substitutional atoms of rare earth occupying the yttrium dodecahedral sites, rare earth and yttrium atoms occupying the aluminum octahedral sites and by another lattice imperfections generated in the process of sample growing. The qualitative analysis based on our exact formula for the diffusion coefficientD allows us to extract the contribution of rare earth atoms substituting the Y atoms toD. Considering the dependence oft _m/L _z ² on the temperature and the ratiol _h/L_z we conclude thatD～T _h ^?4 and that the energy of phonons forming the diffusive maxima ranges from 3.2k _BT_H to 4.2k _BT_H, which is in reasonable agreement with the existing estimates.     

Theoretical analysis of the acoustic phonon limited energy loss rate and relaxation time of hot 2D-excitons in a GaAs-square quantum well (SQW)

The average energy loss rate and relaxation time of non-degenerate 2D-excitons interacting with the deformation- and piezoelectric potential of 3D acoustic bulk phonons are calculated perturbation theoretically as a function of the exciton temperature using the matrix elements previously derived in [1]. The energy loss rate limited by the acoustic deformation potential increases proportional toT ₃ ^7/2 (T ₃ ^3/2 ) if the phonon energy is much larger (smaller) than the thermal energy of the excitons having the temperatureT _e . It is shown, that the phonon wavevector componentq _z perpendicular to the interface of the QW must be taken into account in the calculation of the total excitonic loss rate in order to obtain the energy relaxation time value of 30 ps recently estimated in [2] from photoluminescence intensity measurements.     

Non-Debye behaviours of heat capacities of cubic II–VI materials

On the basis of an appropriate four-oscillator version of a representative dispersion-related hybrid model we perform detailed analyses of isobaric heat capacity data available for cubic ZnS, ZnSe, ZnTe, CdTe, HgSe, and HgTe. Characteristic non-Debye behaviours of the C_p(T) data sets under study, which are manifested above all in form of non-monotonic dependences (maxima) of the respective C_p(T)/T³ curves in the cryogenic region, are described in terms of two Einstein oscillators for short-wave transversal acoustic (TA) phonons in combination with relatively weak components of Debye and non-Debye type due to long-wave acoustic phonons. This prominent non-Debye feature is represented alternatively in the form of non-monotonic dependences (minima) of conventional Debye temperature curves, Θ_D(T). The close correlation between the low-temperature asymptotic (decreasing vs. increasing) sections of Θ_D(T) vs. C_p(T)/T³ curves is described by simple algebraic formulae. The maxima positions of the latter are shown to be nearly proportional to the centre of gravity positions of the respective TA phonon spectra sections. The inherent non-Debye nature of the whole phonon density of states (PDOS) spectra is shown to find its global expression in characteristic snakelike shapes of the equivalent, moment-related phonon energy curves.     

The XPS valence band spectra of Hf metal and HfC x N y O z compounds and the correlation to their superconductivity

The x-ray photoemission spectra of the valence bands of Hf metal and of several HfC _x N _y O _z compounds have been measured and are compared to existing band structure calculations. The density of states at the Fermi energy of the HfC _x N _y O _z compounds correlates strongly to their superconducting transition temperatureT _c . A calculation of theT _c values within the frame work of strong coupling superconductors indicates that the phonon spectrum and the electron phonon interaction is approximately constant within the series HfC _x N _y O _z .     

Interpretation of temperature-dependent thermoelectric power behaviour of La0.67Ba0.33MnO3 manganites

The temperature dependence of the thermoelectric power S(T) in polycrystalline La_0.67Ba_0.33MnO₃ has been investigated. In the ferromagnetic regime, the phonon thermoelectric power is evaluated by incorporating the scattering of phonons with impurities, grain boundaries, charge carriers and phonon. The Mott expression is used to compute the electron diffusive thermoelectric power (S_c^diff.) using Fermi energy as electron-free parameter. The S_c^diff infers linear temperature dependence and S_ph^drag increases exponentially with temperature, which is an artefact of various operating scattering mechanisms. The behaviour of the S(T) is determined by competition among the several operating scattering mechanisms for the heat carriers and a balance between carrier diffusion and phonon drag contributions in the La_0.67Ba_0.33MnO₃. Numerical analysis of thermoelectric power of the present model shows similar results as those revealed from experiments.     

Superconductors containing impurities with crystal-field split energy levels

We investigate theoretically the problem of a superconducting matrix containing paramagnetic rare earth impurities with crystal-field split energy levels. There are two competing mechanisms which change the superconducting transition temperatureT _c. One is inelastic charge scattering of conduction electrons from the aspherical part of the 4f charge distribution, which leads to an increase inT _c similar to that of optical phonons. The other and often predominant mechanism comes from the exchange interaction, which depressesT _c and can be very effective even among non-magnetic levels via off-diagonal matrix elements. Crystalline fields serve to alter the effectiveness of the two kinds of scattering depending upon the symmetry character of the low-lying levels, and in favorable cases one may study separately the effects of the two types of scattering by adding different impurities to a given host. We find that crystal-field levels at energies quite high compared tok _B·T_c can still have an important effect onT _c. It is shown that the crystalline-field splitting should be directly observable as structure in the tunneling characteristics.     

Glassy behaviour of random field Ising spins on Bethe lattice in external magnetic field

The thermodynamics and the phase diagram of random field Ising model (RFIM) on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field (B). A Gaussian distribution of random field (hi) with zero mean and variance hi2 = HR2F is considered. The free-energy (F ), the magnetization (M) and the order parameter (q) are investigated for several values of coordination number (z). The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature TC = J/k and when HRF = 0 for finite z. The free-energy (F) values increase as T increases for different intensities of random field (HRF) and finite z. The internal energy (U) has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field HRF increases. The ferromagnetic (FM)-paramagnetic (PM) phase boundary is clearly observed only when z →∞. While FM-PM-spin glass (SG) phase boundaries are present for finite z. The magnetic susceptibility (χ) shows a sharp cusp at TC in a small random field for finite z and rounded different peaks on increasing HRF.     

Optical phonons in CuAlS2

The optical phonons at k=0 of CuAlS₂ have been investigated by Raman scattering, infrared reflectivity and absorption measurements from 50 to 1000 cm^-1 at T=300 K. Eleven of the thirteen expected optically active phonons have been observed and identified with respect to their symmetry types. The phonon frequencies appear in a range from 498 to 76 cm^-1 with predominant polar modes at 445 and 266 cm^-1. The dielectric dispersion for E ⊥ c and E ∥ c has been determined by Kramers-Kronig integrations.     

Phonon spectra and lattice dynamics of lithium nitride

Lithium nitride, Li₃N, belongs to the hexagonal structure with the symmetry point group D_6h. The structure is ionic with four atoms per unit cell and N^3- coordinated in a regular way with eight Li⁺ ions. Polarized Raman scattering and infrared reflectivity spectra are reported. The frequencies of zone center phonons are determined from a Kramers-Kronig analysis and the oscillator fits to the reflectivity data. A rigid shell model with eight parameters, including the anisotropic polarizability of nitrogen ions, yields an excellent fit to the observed phonon frequencies.     

Raman spectra of single crystals of α-P4S3

Polarization data for the Raman-active k = 0 phonons of single crystals of α-P₄S₃ have been measured at 10 K and at high resolution. Of the 24 external and 60 internal phonons expected for the D_2h factor group of α-P₄S₃ we have observed 16 external and 38 internal phonons. The effect of the layer lattice has been proposed to explain the absence of some expected phonon structure. The present work together with an earlier study of the pressure and temperature dependence of the Raman-active phonons have enabled the 4A₁, A₂ and 5E internal molecular modes to be assigned. The resulting normal coordinates give good fits for the Raman-active bands of the heavy isotope P₄ ³²S₂ ³⁴S and for the mixed chalcogen species P₄S_{3 − x}Se_x.     

Nonlinear dynamics of a two-dimensional lattice

The dynamics of the nonlinear excitations in a two-dimensional (2D) φ⁴-diatomic lattice, with nonlinear on-site electron-phonon coupling at the polarizable ion site has been presented, without considering the self consistent phonon approximation. One of the major results obtained from our calculations is in the understanding of continuous structural phase transition, where we have obtained the minimum in soft mode frequency at a soft mode temperatureT _s (>T _c), not at critical temperatureT _c. This occurs due to the anisotropy of such 2D systems.     

The influence of phonons on quantum diffusion in superconductors

The hopping motion of charged light particles coupled to superconducting electrons as well as to phonons is investigated within the framework of a two-state model. Sufficiently far below the transition temperatureT _c the hopping rate is dominated by one-phonon processes if the static energy shifts between the particle ground states are finite but smaller than twice the BCS energy gap. In the opposite limit of large energy asymmetries phonon coupling does not crucially influence the jump rates. The rôle of nonlinear lattice coupling is investigated.     

Impact of anisotropy on polar optical vibration in a wurtzite cylindrical nanowire with ring geometry

The quasi-confined (QC) phonon modes, surface optical (SO) phonon modes and corresponding Fröhlich-like Hamiltonian in a wurtzite cylindrical nanowire with ring geometry are investigated in the framework of the dielectric continuum model and Loudon’s uniaxial crystal model. Numerical calculations are focused on the dispersion relations of the SO phonons and the electron–SO phonon coupling strength. Results show that there are only two branches of SO phonon modes. The dispersions of the two branches of SO phonon modes are obvious when the phonon wave-number k_z or the azimuthal quantum number m is small. Typical degenerating behavior of the SO modes is evidenced due to the anisotropic effect of wurtzite crystal. Moreover, when k_z or m are large enough, the frequencies of the two branches of SO modes converge to a definite limiting frequency in single planar heterostructure. The calculations of the electron–SO phonon coupling strength reveal that the high-frequency SO modes (SO₊) play a more important role in the coupling strength than the low-frequency ones (SO₋). Furthermore, the long-wavelength SO phonons with small m are the main factor contributing to the electron–phonon interaction.     

A poor man's interpretation of the Nozières-Gallet effect

Summary An interpretation of the effect proposed theoretically by Nozières and Gallet (and experimentally observed in⁴He), according to which the growth ratev of a crystal surface just below the roughening temperatureT _R is approximately linear in the disequilibrium Δμ, is given in terms of the properties of the nucleation process in the presence of a characteristic length l. The physical meaning ofl is the distance over which information can propagate on the surface before a new layer is formed. The nucleation barrier is lowered, because the size of a critical nucleus cannot exceedl, the latter being in turn proportional tov ^−1/2. A self-consistency condition ensues. The effect takes place when the correlation length ξ, which diverges atT _R, becomes comparable tol. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Thermodynamics of phonon-stabilized Fermi distributions with application to uranium

Since phonons are built on the free energy of electrons, their frequencies can be altered by thermal electronic excitations, implying that thermal electronic excitations can alter the phonon entropy. The effect of this extra phonon entropy on electronic distribution functions and thermodynamic properties is calculated in the limit of classical vibrations. The phonon entropy stabilizes electrons above the Fermi level by more than the usual k _B T. The thermodynamic coupling of electron and phonon degrees of freedom allows far more heat capacity than in equivalent independent systems. The method developed is used to explain uranium data from the literature.     

Dynamics of cooperative Jahn-TellerT-systems

We consider a cubic crystal with a triply degenerate electronic ground-state in each unit cell (T-state). A linear Jahn-Teller interaction with acoustic phonons is assumed (T-e coupling). Below a critical temperatureT _c a tetragonal cooperative ordering is established. If a static crystal field splits the electronic states, an anticrossing of the cooperative excitation branches and the phonons in the smallk-regime is found. The resulting mixed modes are calculated (RPA and isotropic Debye model). The dispersion curves are given for specifick-directions and the temperature dependence is discussed.Supported by a grant from the Deutsche Forschungsgemeinschaft     

Electron and phonon effects in superconducting tunnel detectors of x-radiation

Nb/Al/AlO_x/Nb superconducting tunnel junctions were investigated in the role of x-ray detectors. Amplitude spectra of pulses arising upon irradiation of tunnel junctions of different sizes by ⁵⁵Mn x-radiation were recorded at a temperature T=1.4 K. We also analyzed the temporal shape of the pulses. We considered the influence of diffuse motion of nonequilibrium quasiparticles, the inverse tunneling effect, and exchange of 2Δ phonons between electrodes, on the characteristics of the tunnel detectors. It is shown that phonon processes can bring about changes in the amplitude, duration, and polarity of the signal. Fiz. Tverd. Tela (St. Petersburg) 41, 1168–1175 (July 1999)     

Phonon anomalies and structural transition in spin ice Dy2Ti2O7: a simultaneous pressure‐dependent and temperature‐dependent Raman study

We revisit the assignment of Raman phonons of rare‐earth titanates by performing Raman measurements on single crystals of O¹⁸ isotope‐rich spin ice and nonmagnetic pyrochlores and compare the results with their O¹⁶ counterparts. We show that the low‐wavenumber Raman modes below 250 cm⁻¹ are not due to oxygen vibrations. A mode near 200 cm⁻¹, commonly assigned as F_2g phonon, which shows highly anomalous temperature dependence, is now assigned to a disorder‐induced Raman active mode involving Ti⁴⁺ vibrations. Moreover, we address here the origin of the ‘new’ Raman mode, observed below T_C ~ 110 K in Dy₂Ti₂O₇, through a simultaneous pressure‐dependent and temperature‐dependent Raman study. Our study confirms the ‘new’ mode to be a phonon mode. We find that dT_C/dP = + 5.9 K/GPa. Temperature dependence of other phonons has also been studied at various pressures up to ~8 GPa. We find that pressure suppresses the anomalous temperature dependence. The role of the inherent vacant sites present in the pyrochlore structure in the anomalous temperature dependence is also discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Functional derivative of Tc with α2(ω)F(ω) for an anisotropic superconductor

The functional derivative δT_c/δα²(ω)F(ω) of the critical temperature (T_c) with the electron-phonon spectral density (α²(ω)F(ω)) gives information on the effectiveness of various phonon modes in enhancing T_c. For an anisotropic superconductor, it is found that δT_c/δα²(ω)F(ω) goes negative at some small but finite phonon energy. This contrasts with the isotropic case for which it is well known that the functional derivative is positive everywhere. Thus, very low energy phonons reduce T_c in an anisotropic superconductor which is similar to the known effects of static impurities that wash out anisotropy and hence reduce T_c.     

On the electrical resistivity of spin glasses

The resistivity of spin glasses with momentum independent static susceptibility _k = due to the disorder of the spin system and to spin excitations is calculated to lowest order in the temperatureT, and above the freezing temperatureT _f . The diffusive modes proposed by Dzyaloshinskii and Volovik lead for to a resistivity of the form=AT ² –BT ^5/2 with positive coefficientsA andB. TheT ^3/2 contribution observed by Ford and Mydosh can be explained by the existence of ferromagnetic clusters. For, a classical theory with 1 for all excitation energies and with _k = leads to a constant resistivity (the Yosida limit). The observed increase of the resistivity aboveT _f can be explained by rather strong magnetic short range order.SFB 125 Aachen-Jülich-Köln